In a Delta ABC,the value of sin A cos B cos C | vedclass

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(D) Given expression: $E = \sin A \cos B \cos C + \sin B \cos C \cos A + \sin C \cos A \cos B$Factor out $\cos A \cos B \cos C$ from the expression:$E

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$\sin A \sin B \sin C$

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(D) Given expression: $E = \sin A \cos B \cos C + \sin B \cos C \cos A + \sin C \cos A \cos B$Factor out $\cos A \cos B \cos C$ from the expression:$E = \cos A \cos B \cos C \left( \frac{\sin A}{\cos A} + \frac{\sin B}{\cos B} + \frac{\sin C}{\cos C} ight)$$E = \cos A \cos B \cos C (	an A + 	an B + 	an C)$In any $\Delta ABC$,we know that $	an A + 	an B + 	an C = 	an A 	an B 	an C$.Substituting this identity:$E = \cos A \cos B \cos C (	an A 	an B 	an C)$$E = \cos A \cos B \cos C \left( \frac{\sin A}{\cos A} \cdot \frac{\sin B}{\cos B} \cdot \frac{\sin C}{\cos C} ight)$$E = \sin A \sin B \sin C$.

In a $\Delta ABC$,the value of $\sin A \cos B \cos C + \sin B \cos C \cos A + \sin C \cos A \cos B$ is:

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